It is well known that light travels at different speeds in different media. The change of speed results in refraction. Snell's law characterises the behaviour of a light ray which passes from one medium into another medium having a different index of refraction than the first medium. Specifically: EQU n.sub.1 sin.theta..sub.1 =n.sub.2 sin.theta..sub.2 (1)
where, as shown in FIG. 1, n.sub.1 is the index of refraction of the first medium, n.sub.2 is the index of refraction of the second medium, .theta..sub.1 is the angle of incidence (or refraction), within the first medium between the light ray and a normal vector to the interface between the two media, and .theta..sub.2 is the angle of incidence (or refraction), within the second medium between the light ray and the normal.
As shown in FIG. 1, when light ray 10 passes from a higher refractive index medium such as glass, into a lower refractive index medium such as air, ray 10 is refracted away from normal 12. Conversely, if the direction of ray 10 is reversed, such that the ray passes from the lower index medium into the higher index medium, then the ray is refracted toward normal 12.
Thus, when ray 10 exits from the glass into the air, the refracted portion of ray 10 bends away from normal 12. The more the incident portion of ray 10 diverges from normal 12, the more the refracted portion of ray 10 diverges from the normal. Snell's law can be solved as follows to determine the angle .theta..sub.2 at which the refracted portion of ray 10 exits from the glass into the air: ##EQU1##
Sin .theta..sub.1 increases as the incident portion of ray 10 within the glass diverges away from normal 12. The n.sub.1 /n.sub.2 portion of the argument of the arcs in function exceeds 1 (i.e. for glass, n.sub.1.apprxeq.1.5; and, for air n.sub.2.apprxeq.1; so n.sub.1 /n.sub.2.apprxeq.1.5). But the maximum value of the sine function is 1, so the arcs in function does not yield real values for arguments greater than 1. Consequently, if n.sub.1 /n.sub.2 sin.theta..sub.1.gtoreq.1 there is no solution for the refracted angle .theta..sub.2. In practice, TIR occurs if n.sub.1/n.sub.2 sin.theta..sub.1.gtoreq.1, under such circumstances, and the incident light ray is reflected back into the glass. The angle at which TIR first occurs as the refracted portion of ray 10 moves away from normal 12 is called the critical angle .theta..sub.c, given by: ##EQU2##
Equation (3) shows that the size of the critical angle is related to the ratio of the two indices of refraction n.sub.1, n.sub.2. If the ratio of the two indices of refraction is relatively large, then the critical angle will be relatively small (i.e. closer to the normal) and vice versa. For purposes of the present invention, smaller critical angles (and hence a larger ratio of the two indices of refraction) are preferred, since they provide a larger range of angles within which TIR may occur. This means that more incident light can be reflected, and it is consequently possible to provide a display device having an improved range of viewing angles, and/or whiter appearance, both of which are desirable characteristics. It is thus apparent that n.sub.1 is preferably as large as possible, and n.sub.2 is preferably as small as possible.
It is well known that the incident portion of a light ray which undergoes TIR slightly penetrates the interface at which TIR occurs. This so-called "evanescent wave penetration" is of the order of about 0.25 micron for visible light. By interfering with (i.e. scattering and/or absorbing) the evanescent wave one may prevent or "frustrate" TIR. Specifically, one may frustrate TIR by changing the index of refraction in the vicinity of the evanescent wave. This can be accomplished by introducing into the evanescent wave a light absorptive material; or, by introducing into the evanescent wave a non-light absorptive material having an inhomogeneous refractive index. Inhomogeneity is important in the case of non-absorbent materials. For example, introduction of a homogeneous, finely dispersed particulate non-absorbent material into the evanescent wave would change the refractive index slightly to a value equivalent to that of the opposing medium. This would not prevent TIR, but would merely create an adjacent boundary layer at which TIR would occur.
As explained in U.S. Pat. No. 6,064,784 issued May, 16, 2000 an electrophoretic medium can be used to controllably frustrate TIR in an image display device employing prismatic reflective surfaces. "Electrophoresis" is a well known phenomenon whereby a charged species (i.e. particles, ions or molecules) moves through a medium due to the influence of an applied electric field. For purposes of the present invention, a preferred electrophoretic medium is Fluorinert.TM. Electronic Liquid FC-72 (n.apprxeq.1.25) or FC-75 (n.apprxeq.1.27) heat transfer media available from 3M, St. Paul, Minn. However, it is apparent that even this relatively low refractive index (i.e. compared to n.apprxeq.1.33 for a typical organic solvent electrophoretic medium such as acetonitrile) is insufficient to attain a large refractive index ratio relative to conventional plastic media having refractive indices within the range of about 1.5 to 1.7 (such as polycarbonate, for which n.apprxeq.1.59). In particular, the index ratio in such case is n.sub.2 /n.sub.1 =1.59/1.27.apprxeq.1.25, which corresponds to a relatively high critical angle of 53.degree. required to achieve TIR at such an interface.
To achieve the desired high critical angle relative to a Fluorinert.TM. electrophoretic medium, the adjacent material (assumed to be a prismatic material bearing isosceles right angle prisms) must have a refractive index of at least n.sub.1 =2.multidot.n.sub.2 =2.multidot.1.27.apprxeq.1.8, which is unachievable with inexpensive plastic materials. Indeed, the adjacent material's refractive index should preferably be about 2.0 to facilitate TIR of light rays which are incident upon the surface of the image display within a range of angles close to, but not precisely normal to the surface of the display. There are ceramic materials with refractive indices substantially greater than 1.8. However, it is difficult and expensive to micro replicate prismatic surfaces on such materials.
The present invention overcomes the foregoing difficulties.